Calibration optic for a solar/earth spectrometer

ABSTRACT

A system for calibrating a spectrometer includes wide field-of-view (WFOV) optics providing a first light path to a WFOV spectrometer, and narrow field-of-view (NFOV) optics providing a second light path to a NFOV spectrometer. A de-focusing optic is selectively positioned in the first or second light paths. A scan controller selectively controls the WFOV or NFOV optics to scan a celestial body. A processor is configured to calibrate the de-focusing optic, while the WFOV optics scan the celestial body. First, the WFOV optics scan the celestial body without the de-focusing optic positioned in the first light path. Second, the WFOV optics scan the celestial body with the de-focusing optic positioned in the first light path. Next, the processor calibrates the NFOV spectrometer, while the NFOV optics and the de-focusing optic scan the celestial body. After the NFOV spectrometer is calibrated, the NFOV spectrometer may be used to measure the albedo of the earth.

TECHNICAL FIELD

The present invention relates, in general, to the field of radiometryand, more specifically, to a system and method for radiometriccalibration of climate monitoring remote sensors in space, employingsolar radiation as a source.

BACKGROUND OF THE INVENTION

Space based planetary imagers are useful for remote sensing ofatmospheric compositions, crop assessments, weather prediction and othertypes of monitoring activities. Monochromatic and multispectralsatellite-based, remote sensors are able to measure properties of theatmosphere above the earth, when their detector arrays are properlycalibrated for radiometric response.

A method of calibrating the radiance measured by these remote sensors isto create a reference radiation using a known source of spectralradiance, such as the sun. The radiation from the sun may be used as areference signal to a diffusive reflector which, in turn, may provide aknown radiance to a remote sensor for calibrating its detector arrays.

The output of the detector arrays may be measured as the remote sensorreceives the known reflected energy from the diffusive reflector. Thisradiance calibration method provides sufficient information to correctlymeasure and calculate other types of radiance incident on the remotesensor during normal operation, such as radiance from views of the earthor other targets of interest.

The spectral characteristics of a diffusive reflector, or diffuserpanel, however, may change with time due to degradation of the diffuserpanel. Since the diffuser panel is employed as the reference source, anychange, i.e., degradation of the diffusive surface material, results ina distortion in the measurement of the remote sensor.

Other diffusers, such as transmissive diffusers (for example screen orpinhole arrays) also have disadvantages. Screens or pinhole arrays havegeometries that may cause undesired diffraction effects. Screens arealso difficult to calibrate over ranges of angles, due to thethree-dimensional nature of the screens, which may cause internalshadowing. Furthermore, pinholes are subject to clogging from extraneousminute particles.

The present invention provides a diffuser, referred to herein as ade-focusing optic, for an earth viewing solar wavelength spectrometer(such as the Climate Absolute Radiance and Refractivity Observatory(CLARREO)) so that it may stare straight at the sun without saturating.Moreover, the use of convolution integrals by the present inventionallows direct in-flight measurements of the de-focused spectrometer'sspectral throughput. As will be explained, the sun may thus be used as acalibration target for the spectrometer.

SUMMARY OF THE INVENTION

To meet this and other needs, and in view of its purposes, the presentinvention provides a system for calibrating a spectrometer. The systemincludes wide field-of-view (WFOV) optics providing a first light pathto a first spectrometer, and narrow field-of-view (NFOV) opticsproviding a second light path to a second spectrometer. A de-focusingoptic is selectively positioned in the first or second light paths. Ascan controller selectively controls the WFOV or NFOV optics to scan acelestial body. A processor is configured to calibrate the de-focusingoptic, when the WFOV optics scan the celestial body. The processor isalso configured to calibrate the second spectrometer, when the NFOVoptics and the de-focusing optic scan the celestial body.

The processor is configured to calibrate the de-focusing optic, when (a)the WFOV optics scan the celestial body without the de-focusing opticpositioned in the first light path, and (b) the WFOV optics scan thecelestial body with the de-focusing optic positioned in the first lightpath. The processor is configured to calibrate the second spectrometer,after the processor calibrates the de-focusing optic. The scancontroller is also configured to control the NFOV optics to scan theearth, in addition to the celestial body. The celestial body may includethe sun or the moon.

The scan controller is configured to provide azimuth and elevationcontrol for raster scanning the celestial body. A two sided mirror isincluded with one side for reflecting received light in the first lightpath to the first spectrometer, and another side for reflecting receivedlight in the second light path to the second spectrometer. Thede-focusing optic includes one or more of an un-polarized diffuser, aP-polarized diffuser and an S-polarized diffuser. The de-focusing opticis positioned on a circumferential casing of a housing, and is rotatableabout the circumferential casing for selectively positioning thede-focusing optic in the first or second light paths.

The NFOV optics and the WFOV optics are oriented to receive light fromtwo opposing directions. When the NFOV optics receives light from thesun, concurrently, the WFOV optics may receive light from the earth.

The present invention includes a method of calibrating a radiometricsystem. The method includes the steps of:

(a) scanning a celestial body using WFOV optics;

(b) scanning the celestial body using NFOV optics;

(c) selectively positioning a de-focusing optic to intercept lightreceived by the WFOV optics and light received by the NFOV optics;

(d) calibrating the de-focusing optic using steps (a) and (c); and

(e) calibrating a NFOV imager using steps (b) and (c).

The method of the invention also includes imaging the earth, aftercalibrating the NFOV imager. The steps of scanning include rasterscanning the celestial body in azimuth and elevation angles. Scanningthe celestial body includes scanning the sun or the moon, while orbitingthe earth.

Calibrating the de-focusing optic includes the steps of: (i) calibratinga WFOV imager, with the de-focusing optic positioned not to interceptlight received by the WFOV optics, and (ii) calibrating both the WFOVimager and the de-focusing optic, with the de-focusing optic positionedto intercept light received by the WFOV optics, and (iii) calculating aratio between values obtained in steps (i) and (ii). Calibrating theNFOV imager includes the step of: calibrating the NFOV imager, afterperforming step (d) above.

Yet another embodiment of the present invention is a method for animager to view a celestial body. The method includes the steps of: (a)scanning the celestial body with a predetermined FOV; (b) orbiting theearth, while the celestial body is scanned in step (a) to provide anelevation motion to the FOV; and (c) rotating the FOV back and forth, toprovide an azimuth motion to the FOV. Steps (b) and (c) are effective inproviding a raster scan of the celestial body. The method furtherincludes the step of: (d) determining intensity output of the imager byintegrating data obtained by the imager, while raster scanning thecelestial body over angular space. Determining intensity output of theimager includes multiplying (i) an integral of a point spread function(PSF) of a detector output of the imager at a predetermined wavelengthwith (ii) an integral of a radiant output of a known source at thepredetermined wavelength. The integral of the PSF and the integral ofthe radiant output are calculated while orbiting a hemisphere of theearth.

The method also includes the steps of: (i) inserting a de-focusing opticin a received light path of the imager and determining the intensityoutput of the imager, and (ii) removing the de-focusing optic from thereceived light path of the imager and determining the intensity outputof the imager.

It is understood that the forgoing general description and the followingdetailed description are exemplary, but are not restrictive, of theinvention.

BRIEF DESCRIPTION OF THE FIGURES

The invention may be understood from the following detailed descriptionwhen read in connection with the accompanying figures:

FIG. 1 a is a perspective view of the CERES instrument in a fixedelevation, and rotating, back and forth, in azimuth to provide a rasterscan of the moon.

FIG. 1 b is a functional view of the azimuth and elevation anglesprovided of the lunar raster scan by the CERES instrument shown in FIG.1 a.

FIG. 1 c is an exemplary radiative output of a short wave (SW) detectorin the CERES instrument during its lunar raster scan.

FIG. 2 is a functional block diagram of a radiometric system inaccordance with an embodiment of the present invention.

FIG. 3 is a functional view of a wide field-of-view (WFOV) spectrometerand a narrow field-of-view (NFOV) spectrometer for viewing a planetarybody, such as the sun, through the same de-focusing optic (or diffuser)disposed in the system of FIG. 2, in accordance with an embodiment ofthe present invention.

FIG. 4 a is a cross-sectional view of a two sided mirror for receivinglight from WFOV optics and NFOV optics disposed in the system of FIG. 2,in accordance with an embodiment of the present invention.

FIG. 4 b is a cross-sectional view of the back-and-forth azimuthrotation at a fixed elevation angle for the WFOV and NFOV opticsdisposed in the system of FIG. 2, in accordance with an embodiment ofthe present invention.

FIG. 4 c is a pictorial view of the CLARREO instrument performing rasterscan of the sun as it orbits the earth.

FIG. 5 a is a top view of a two sided mirror surrounded by a casing of aradiometric system, which includes three different diffusers which maybe rotated in elevation about a NFOV telescope and a WFOV telescope, inaccordance with an embodiment of the present invention.

FIG. 5 b is a side view of the two sided mirror shown in FIG. 5 a.

FIG. 5 c is an front view of the two sided mirror shown in FIG. 5 a.

FIG. 6 is a flow diagram of a method of calibrating the NFOVspectrometer shown in the radiometric system of FIG. 2, in accordancewith an embodiment of the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The present invention provides a de-focusing optic for an earth viewingsolar wavelength spectrometer (such as the Climate Absolute Radiance andRefractivity Observatory (CLARREO)) so that it may stare straight at thesun without saturating. Moreover, the use of convolution integrals bythe present invention allows direct in-flight measurements of thede-focused spectrometer's spectral throughput. The sun may thus be usedas a calibration target for the spectrometer.

The following explains a calibration measurement of response of awavelength dependent spectrometer, by using a solar wavelengthcalibration source of known radiant output L^(s)(λ) which has a uniformspatial extent that overfills a telescope's field-of-view (FOV). In aground calibration, the telescope scans and stares at the calibrationsource for several seconds. With source uniformity, Eqn. 1 representsthe spectrometer signal at detector k of a CCD array (i.e. where k isproportional to wavelength λ). Since the source radiance is known, theinstrument channel's radiometric gain G_(k) may be found using Eqn. 2:

$\begin{matrix}{V_{k} = {g_{k} \times {L^{s}\left( \lambda_{k} \right)} \times {\int_{0}^{2\;\pi}{{P_{k}\left( {\theta,\phi} \right)}\ {\mathbb{d}\Omega}}}}} & (1) \\{G_{k} = \frac{V_{k}}{L^{s}\left( \lambda_{k} \right)}} & (2) \\{= {g_{k}{\int_{0}^{2\pi}{{P_{k}\left( {\theta,\phi} \right)}\ {\mathbb{d}\Omega}}}}} & (3)\end{matrix}$

In the above equations, ‘g_(k)’ is a constant that gives the detectoroutput per unit quantity of radiance at wavelength λ_(k) when convertedinto electrons in the CCD pixel. Furthermore, P_(k)(θ,φ) is the combinedtelescope and detector field-of-view response, which may be referred toas a point spread function (PSF) for pixel k (and hence wavelengthλ_(k)). This gain value may then be used to convert earth viewingdetector counts into measurements of overfilled, unfiltered radiancefrom scene ‘i’ for wavelength λ_(k) as in Eqn. 4:

$\begin{matrix}{{L^{i}\left( \lambda_{k} \right)} = \frac{V_{k}}{G_{k}}} & (4)\end{matrix}$

For a spectrometer ‘q ’, the PSF of detector k may be found, as shown inthe equations below, by the convolution of the detector's spatialresponse D_(k) ^(q)(θ,φ) with the telescope's modular transfer function(MTF_(k) ^(q), which is the Fourier transform of the telescope's spatialtransfer function

$\left\lbrack {\sqrt{\alpha_{k}^{q}} \times {t_{k}^{q}\left( {x,y} \right)} \times {\mathbb{e}}^{z_{k}^{q}{({x,y})}}} \right\rbrack.$It will be appreciated that t_(k) ^(q)(x,y) is entirely real and z_(k)^(q)(x,y) is entirely imaginary:

$\begin{matrix}{{{MTF}_{k}^{q}\left( {\theta,\phi} \right)} = {{FT}\left\lbrack {\sqrt{\alpha_{k}^{q}} \times {t_{k}^{q}\left( {x,y} \right)} \times {\mathbb{e}}^{z_{k}^{q}{({x,y})}}} \right\rbrack}} & (5) \\{{\int_{0}^{2\pi}{{D_{k}^{q}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}} = 1} & (6) \\{{P_{k}^{q}\left( {\theta^{\prime},\phi^{\prime}} \right)} = {\int_{0}^{2\pi}{{D_{k}^{q}\left( {\theta,\phi} \right)}{{{MTF}_{k}^{q}\left( {{\theta - \theta^{\prime}},{\phi - \phi^{\prime}}} \right)}}^{2}{\mathbb{d}\Omega}}}} & (7) \\{{P_{k}^{q}\left( {\theta,\phi} \right)} = {{D_{k}^{q}\left( {\theta,\phi} \right)} \otimes {{{MTF}_{k}^{q}\left( {\theta,\phi} \right)}}^{2}}} & (8) \\{{{FT}\left\lfloor {t_{k}^{q}\left( {x,y} \right)} \right\rfloor} = {T_{k}^{q}\left( {\theta,\phi} \right)}} & (9) \\{{{FT}\left\lbrack {\mathbb{e}}^{z_{k}^{q}{({x,y})}} \right\rbrack} = {Z_{k}^{q}\left( {\theta,\phi} \right)}} & (10) \\{{\int_{- \infty}^{\infty}{{{{t_{k}^{q}\left( {x,y} \right)}{\mathbb{e}}^{z_{k}^{q}{({x,y})}}}}^{2}\ {\mathbb{d}x}{\mathbb{d}y}}} = {\int_{0}^{2\pi}{{{{T_{k}^{q}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{q}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}} & (11) \\{= 1} & (12) \\{{P_{k}^{q}\left( {\theta,\phi} \right)} = {\alpha_{k}^{q} \times {{D_{k}^{q}\left( {\theta,\phi} \right)} \otimes {{{T_{k}^{q}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{q}\left( {\theta,\phi} \right)}}}^{2}}}} & (13) \\{{\frac{V_{k}^{q}\left( {\theta_{t},\phi_{t}} \right)}{\cos\;\theta_{t}} = {{g_{k}^{q} \times {{P_{k}^{q}\left( {\theta,\phi} \right)} \otimes {L_{k}^{s}\left( {\theta_{t},\phi_{t}} \right)}}} = {g_{k}^{q} \times \alpha_{k}^{q} \times {{D_{k}^{q}\left( {\theta,\phi} \right)} \otimes {L_{k}^{s}\left( {\theta_{t},\phi_{t}} \right)} \otimes {{{T_{k}^{q}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{q}\left( {\theta,\phi} \right)}}}^{2}}}}}\mspace{25mu}} & \begin{matrix}(14) \\(15)\end{matrix}\end{matrix}$The property of Eqns. 11 and 12 allows the factor α_(k) ^(q) torepresent the fractional degradation of spectrometer q at wavelengthλ_(k). Eqn 14 shows how the detector output is the result of aconvolution in angular space between the PSF, P_(k) ^(q)(θ,φ), and thecelestial body radiance L_(k) ^(s)(θ,φ). It will be understood that(θ,φ) are, respectively, angles of elevation and azimuth.

In the event that the telescope raster scans a celestial body, like thesun or moon, as in the Clouds and the Earth's Radiant Energy System(CERES) shown in FIGS. 1 a and 1 b, then the detector signal at time tmay be found from Eqn. 15. In the example shown in FIG. 1 b, CERES israster scanning the moon, and providing the detector results shown inFIG. 1 c, (L_(k) ^(s)(θ,φ) is the spatially resolved radiance from themoon at wavelength λ_(k) and time ‘t’).

This allows use of a mathematical property shown below that the integralof a function which is itself the convolution of multiple functions,gives the product of each function's integral (so long as both functionsare non-zero for a finite range):

$\begin{matrix}{\Gamma = {\int_{- \infty}^{\infty}{\int_{- \infty}{{X\left( t^{\prime} \right)}{Y\left( {t - t^{\prime}} \right)}{\mathbb{d}t^{\prime}}{\mathbb{d}t}}}}} & (16) \\{= {\int_{- \infty}^{\infty}{{{X(t)} \otimes {Y(t)}}{\mathbb{d}t}}}} & (17) \\{= {\int_{- \infty}^{\infty}{{X(t)}{\mathbb{d}t} \times {\int_{- \infty}^{\infty}{{Y(t)}{\mathbb{d}t}}}}}} & (18)\end{matrix}$With this property of convolution integrals, it is possible to use therepresentation of an integral of raster scan data of a spectrometer ‘q’over angular space, as shown below:

$\begin{matrix}{F_{k}^{q} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{q}\left( {\theta,\phi} \right)}{\cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (19) \\{= {g_{k}^{q}{\int_{0}^{2\pi}{{P_{k}^{q}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega} \times {\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}}}}} & (20) \\{{g_{k}^{q}{\int_{0}^{2\pi}{{P_{k}^{q}\left( {\theta,\phi} \right)}\ {\mathbb{d}\Omega}}}} = G_{k}^{q}} & (21) \\{F_{k}^{q} = {G_{k}^{q}{\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}}} & (22)\end{matrix}$

If the integration of Eqn. 19 is performed on a detector output (forexample a CLARREO detector, or a CERES detector) from a celestial bodyraster scan, the result is the radiometric gain G_(k) (Eqns. 3 and 21)multiplied by the disk integrated radiance from the celestial body ‘s’,as in Eqn. 22 (for example, the moon in a raster scan by CERES, or thesun in a raster scan by CLARREO).

If R_(eq) & R_(pol) are the equatorial and polar radius of the celestialbody and D_(sb) is the satellite's distance, Eqn. 23 provides theangular extent of the celestial body, such as the sun or moon. This maybe used in Eqn. 24 to give the mean radiance ‘ρ_(k)’ leaving thecelestial body surface:

$\begin{matrix}{{\Delta\Omega}_{s} = {2{\pi\left( {1 - \sqrt{1 - \frac{R_{eq}R_{pol}}{D_{sb}^{2}}}} \right)}}} & (23) \\{\rho_{k} = \frac{F_{k}^{q}}{G_{k}^{q} \times {\Delta\Omega}_{s}}} & (24)\end{matrix}$

As will be explained, the present invention advantageously accounts forlack of precise knowledge of the shape of the PSF. It also provides anadvantage that by integrating over thousands of samples, the signal tonoise of ‘ρ_(k)’ is significantly increased. This may be seen byreferring to FIG. 1 c, in the lunar example, which shows the lunarradiance produces a small signal from the CERES short wave (SW) detectorof approximately 35 counts, as compared to a 1000 counts from a typicalearth scene.

Referring next to FIG. 2, there is shown a radiometric system, generallydesignated as 20. Radiometric system 20 may be a modified CLARREOsystem. As shown, system 20 includes wide FOV (WFOV) optics 21 (or WFOVtelescope 21) and narrow FOV (NFOV) optics 27 (or NFOV telescope 27),which are both positioned in azimuth and/or elevation by a gimballedplatform 24. The WFOV optics are coupled to spectrometer 23 and the NFOVoptics are coupled to spectrometer 28. Both spectrometers includedetector arrays for, respectively, imaging the sun (through the WFOVoptics) and imaging the sun or the earth (through the NFOV optics). Amicroprocessor or a controller, designated as 26, may be used to controlgimballed platform 24 for raster scanning the sun using the WFOV optics,and raster scanning the sun/earth using the NFOV optics.

A de-focusing optic, generally designated as 22, is used to diffuse thelight received through the WFOV optics and distribute that receivedthrough the NFOV optics. The microprocessor 26, by way of motor 25, maybe used to position de-focusing optic 22 so that it intercepts the lightfrom the WFOV optics or intercepts the light from the NFOV optics.Although not shown, it will be appreciated that de-focusing optic 22 mayalso have a stowed position, in which the optics may view an object ofinterest without diffusing the received light paths.

Referring now to FIG. 3, there are shown the WFOV and NFOV spectrometersin which both may view the sun through the same de-focusing optic(diffuser), or through the same SIDCO. As used herein, SIDCO refers tothe solar intensity distributing and convolving optic (same as optic 22)that may be used as a de-focusing optic in CLARREO. The WFOVspectrometer may view the sun directly through the SIDCO to measure thedesired solar spectrum. The NFOV spectrometer may also view the sundirectly through the same SIDCO to measure the desired solar spectrum;and measure the earth's albedo without the SIDCO in its path.

The field stops shown in FIG. 3 may be used by the present invention toprevent photons scattered from the spectrometer's front optic fromre-entering the telescope.

An embodiment of the scanhead including the WFOV telescope and the NFOVtelescope is shown in FIGS. 4 a and 4 b. As shown, light received by theWFOV telescope and light received by the NFOV telescope are reflected bya two-sided 45 degree mirror. One side of the mirror reflects thereceived light toward the WFOV spectrometer and the other side of themirror reflects the received light toward the NFOV spectrometer.Referring to FIG. 4 b, both telescopes are shown housed within anencased housing of the radiometric system (for example CLARREO). TheWFOV and NFOV telescopes may be rotated in azimuth at a fixed elevation,as shown in FIG. 4 b. At fixed elevation angles, the casing of thehousing includes three SIDCO optics for de-focusing either the WFOVoptics or the NFOV optics, when raster scanning the sun. The de-focusingmay be accomplished through one of three SIDCO optics, which are shownfixed at three different elevation angles. One SIDCO optic isun-polarized and the other two optics are either S-polarized orP-polarized.

In operation, radiometric system 20, shown in FIG. 2, may be encased inthe housing of CLARREO. If the WFOV telescope is to view the sun througha SIDCO, the telescope's scanhead may be rotated in elevation to viewthe sun through one of the three SIDCO optics. Similarly, if the NFOVtelescope is to view the sun through a SIDCO, the telescope's scanheadmay be rotated in elevation to view the sun through one of the threesame SIDCO optics. Once the telescope's scanhead is fixed in elevation,the WFOV telescope, or the NFOV telescope may be rotated back and forthin azimuth, as shown in FIG. 4 b. Thus, three calibrations may beperformed using the WFOV telescope with the three respective SIDCOoptics. Similarly, three other calibrations may be performed using theNFOV telescope with the same three respective SIDCO optics.

When the calibrations are completed, the NFOV telescope may bepositioned at a fixed elevation angle, so that it may view the earthwithout interference from any one of the three SIDCO optics.

The raster scan of the sun (for example) is best performed as shown inFIG. 4 c, with either the WFOV or NFOV telescope in use while the moonis behind the earth. It will be appreciated that each raster scan of thesun is performed by the present invention on one orbit of theradiometric system (for example CLARREO), as the system moves from thenorth pole to the south pole on the earth's orbit. It will also beappreciated that although the telescope views the sun at a fixedelevation angle, nevertheless, a raster scan is provided by the presentinvention, similar to the raster scan shown in FIG. 1 b. The raster scanis shown moving in elevation, because the radiometric system is movingin orbit around the earth.

Yet another embodiment of the present invention is provided in FIGS. 5a, 5 b and 5 c. As shown, an un-polarized diffuser, a P-polarizeddiffuser and an S-polarized is diffuser are configured to be rotated inelevation so that each may be viewed through the WFOV or NFOV optics.This may be accomplished, as shown, by using two separately rotatabledrums. A two sided mirror is shown positioned at 45 degrees, so that theWFOV telescope may view the sun through one of the three diffusers, andconcurrently, the NFOV telescope may view the earth without a diffuserin its path.

The calibration procedure is discussed next. A direct view of the sunusing the WFOV optics, without an interfering SIDCO optic, is performedduring an earth orbit by CLARREO (for example) to provide the followingresult (where α_(k) ^(w) represents the fractional degradation of theWFOV optics):

$\begin{matrix}{F_{k}^{w} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{w}\left( {\theta,\phi} \right)}{\cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (25) \\{= {g_{k}^{w} \times \alpha_{k}^{w} \times {\int_{0}^{2\pi}{{D_{k}^{w}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}{\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}{\int_{0}^{2\pi}{{{{T_{k}^{w}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{w}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}}}}}}} & (26) \\{= {g_{k}^{w} \times \alpha_{k}^{w} \times {\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}}} & (27)\end{matrix}$

Next, if a raster scan of the sun is completed on the next orbit ofCLARREO using the WFOV optics, but this time also using one of the threeSIDCO optics, then the result is modified, because of a change in thePSF of the instrument (i.e. now the WFOV telescope and the SIDCO opticshave a combined modulation transfer function (DMTF_(k) ^(wd), q=wd,where the diffuser (or SIDCO) has transmission

$\begin{matrix}{\left. {\sqrt{\beta_{k}} \times {n_{k}\left( {x,y} \right)} \times {\mathbb{e}}^{\delta_{k}{({x,y})}}} \right):} & \; \\{{{DMTF}_{k}^{wd}\left( {\theta,\phi} \right)} = {{FT}\left\lbrack {\sqrt{\alpha_{k}^{w}} \times {t_{k}^{w}\left( {x,y} \right)} \times {\mathbb{e}}^{z_{k}^{w}{({x,y})}} \times \sqrt{\beta_{k}} \times {n_{k}\left( {x,y} \right)} \times {\mathbb{e}}^{\delta_{k}{({x,y})}}} \right\rbrack}} & (28) \\{{{FT}\left\lbrack {n_{k}\left( {x,y} \right)} \right\rbrack} = {N_{k}\left( {\theta,\phi} \right)}} & (29) \\{{{FT}\left\lfloor {\mathbb{e}}^{\delta_{k}{({x,y})}} \right\rfloor} = {\Delta_{k}\left( {\theta,\phi} \right)}} & (30) \\{{\int_{- \infty}^{\infty}{{{{n_{k}\left( {x,y} \right)}{\mathbb{e}}^{\delta_{k}{({x,y})}}}}^{2}{\mathbb{d}x}{\mathbb{d}y}}} = {\int_{0}^{2\pi}{{{{N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}} & (31) \\{= 1} & (32) \\{\frac{V_{k}^{wd}\left( {\theta_{t},\phi_{t}} \right)}{\cos\;\theta_{t}} = {g_{k}^{w} \times {{D_{k}^{w}\left( {\theta,\phi} \right)} \otimes {L_{k}^{s}\left( {\theta_{t},\phi_{t}} \right)} \otimes {{{DMTF}_{k}^{wd}\left( {\theta,\phi} \right)}}^{2}}}} & (33) \\{= {g_{k}^{w} \times \alpha_{k}^{w} \times \beta_{k} \times {{D_{k}^{w}\left( {\theta,\phi} \right)} \otimes {L_{k}^{s}\left( {\theta_{t},\phi_{t}} \right)} \otimes {{{T_{k}^{w}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{w}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}}}} & (34)\end{matrix}$

It is important to point out that the presence of Δ_(k)(θ,φ) in Eqn. 34has the effect of de-focusing sunlight over an entire hemisphere andhence attenuating the solar radiance L_(k) ^(s)(θ,φ). Next, anintegration of this signal over a 2π hemisphere and a ratio with theresult of Eqn. 27, yields the following:

$\begin{matrix}{F_{k}^{wd} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{wd}\left( {\theta,\phi} \right)}{\cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (35) \\{= {g_{k}^{w} \times \alpha_{k}^{w} \times \beta_{k}{\int_{0}^{2\pi}{{D_{k}^{w}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}{\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}{\int_{0}^{2\pi}{{{{T_{k}^{w}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{w}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}}}}}}} & (36) \\{= {g_{k}^{w} \times \alpha_{k}^{w} \times \beta_{k}{\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}{\int_{0}^{2\pi}{{{{T_{k}^{w}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{w}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}}}}} & (37) \\{R_{k} = \frac{F_{k}^{wd}}{F_{k}^{w}}} & (38) \\{= {\beta_{k} \times \sigma_{k}}} & (39) \\{\sigma_{k} = {\int_{0}^{2\pi}{{{{T_{k}^{w}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{w}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}} & (40)\end{matrix}$

The ratio with cos θ in Eqn. 35 requires that the radiometric system beequipped with sufficient baffling, so that the response may fall to zeroas the elevation angle of θ→π/2. This prevents amplification of noise inthe signal for far off-axis counts. Given a typical transmission β_(k)of 0.5, the telescope response for θ>60° may fall to zero and stillprovide a 10⁻⁵ attenuation of the solar signal.

Next, the NFOV telescope is used to raster scan the sun through the sameSIDCO optics (q=nd) to obtain:

$\begin{matrix}{{{DMTF}_{k}^{nd}\left( {\theta,\phi} \right)} = {{FT}\left\lbrack {\sqrt{\alpha_{k}^{n}} \times {t_{k}^{n}\left( {x,y} \right)} \times {\mathbb{e}}^{z_{k}^{n}{({x,y})}} \times \sqrt{\beta_{k}} \times {n_{k}\left( {x,y} \right)} \times {\mathbb{e}}^{\delta_{k}{({x,y})}}} \right\rbrack}} & (41) \\{{{FT}\left\lfloor {t_{k}^{n}\left( {x,y} \right)} \right\rfloor} = {T_{k}^{n}\left( {\theta,\phi} \right)}} & (42) \\{{{FT}\left\lbrack {\mathbb{e}}^{z_{k}^{n}{({x,y})}} \right\rbrack} = {Z_{k}^{n}\left( {\theta,\phi} \right)}} & (43) \\{{\int_{- \infty}^{\infty}{{{{t^{n}\left( {x,y} \right)}{\mathbb{e}}^{z_{k}^{n}{({x,y})}}}}^{2}\ {\mathbb{d}x}{\mathbb{d}y}}} = {\int_{0}^{2\pi}{{{{T_{k}^{n}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{n}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}} & (44) \\{= 1} & (45) \\{\frac{V_{k}^{nd}\left( {\theta_{t},\phi_{t}} \right)}{\cos\;\theta_{t}} = {g_{k}^{n} \times {{D_{k}^{n}\left( {\theta,\phi} \right)} \otimes {L_{k}^{s}\left( {\theta_{t},\phi_{t}} \right)} \otimes {{{DMTF}_{k}^{nd}\left( {\theta,\phi} \right)}}^{2}}}} & (46) \\{= {g_{k}^{n} \times \alpha_{k}^{n} \times \beta_{k} \times {{D_{k}^{n}\left( {\theta,\phi} \right)} \otimes {L_{k}^{s}\left( {\theta_{t},\phi_{t}} \right)} \otimes {{{T_{k}^{n}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{n}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}}}} & (47) \\{F_{k}^{nd} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{nd}\left( {\theta_{t},\phi} \right)}{\cos\;\theta} \right\rbrack{\mathbb{d}\;\Omega}}}} & (48) \\{= {\mu_{k} \times g_{k}^{n} \times \alpha_{k}^{n} \times \beta_{k} \times {\int_{0}^{2\pi}{{D_{k}^{n}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}{\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}}}}} & (49) \\{= {\mu_{k} \times g_{k}^{n} \times \alpha_{k}^{n} \times \beta_{k} \times {\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}}} & (50) \\{\mu_{k} = {\int_{0}^{2\pi}\mspace{7mu}{{{{T_{k}^{n}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{n}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}} & (51)\end{matrix}$If the ratio η_(k)=μ_(k)σ_(k) is known, the spectral response of theearth's viewing NFOV may be accurately updated in flight as:

$\begin{matrix}{\eta_{k} = \frac{\int_{0}^{2\pi}{{{{T_{k}^{n}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{n}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}{\int_{0}^{2\pi}{{{{T_{k}^{w}\left( {\theta,\phi} \right)} \otimes {Z_{k}^{w}\left( {\theta,\phi} \right)} \otimes {N_{k}\left( {\theta,\phi} \right)} \otimes {\Delta_{k}\left( {\theta,\phi} \right)}}}^{2}{\mathbb{d}\Omega}}}} & (52) \\{\alpha_{k}^{n} = {\int_{0}^{2\pi}{{P_{k}^{n}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}} & (53) \\{G_{k}^{n} = {F_{k}^{nd} \times \left\lbrack {R_{k} \times \eta_{k} \times {\int_{0}^{2\pi}{{L_{k}^{s}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}} \right\rbrack^{- 1}}} & (54) \\{= {g_{k}^{n} \times {\int_{0}^{2\pi}{{P_{k}^{n}\left( {\theta,\phi} \right)}{\mathbb{d}\Omega}}}}} & (55)\end{matrix}$

The ratio η_(k) in Eqn. 52 is likely resistant to change due to opticaldegradation. Therefore, with a ground measurement of η_(k) (using afacility such as the SIRCUS calibration system, as described below) thepresent invention provides accurate and stable spectral measurements ofthe earth's albedo.

Accuracy of CLARREO's albedo measurement using a SIDCO of the presentinvention relies on a high quality ground determination of the ratioη_(k) and on limiting any mechanical deformations of the telescopesystem during launch. Stability depends on how much this ratio maypotentially change in flight, due to non-uniform degradation of theCLARREO optics and any change to optical alignment or aberration due tothermal expansion/contraction of the telescope system.

Ground measurement of η_(k) may be performed on a completed instrumentsystem, such as CLARREO, using uniform and collimated laser radianceL_(k) ^(C) from the SIRCUS calibration system, such that the radianceoverfills the telescope's entrance aperture. The instrument system thenneeds to be mounted on a one-dimensional gimbal so the angle of laserentry may be varied across an entire hemisphere (re-creating theon-orbit scan conditions shown in FIGS. 1 a, 1 b and 4 c). The ratioη_(k) may then be determined by making four ground measurements. Thesemeasurements may be done on both the NFOV and WFOV spectrometer signalswith the SIDCO in and out of place (i.e. V^(nd), V^(n), V^(wd), V^(w)):

$\begin{matrix}{C_{k}^{nd} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{nd}\left( {\theta_{t},\phi_{t}} \right)}{{L_{k}^{C}(t)} \times \cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (56) \\{C_{k}^{n} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{n}\left( {\theta_{t},\phi_{t}} \right)}{{L_{k}^{C}(t)} \times \cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (57) \\{C_{k}^{wd} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{wd}\left( {\theta_{t},\phi_{t}} \right)}{{L_{k}^{C}(t)} \times \cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (58) \\{C_{k}^{w} = {\int_{0}^{2\pi}{\left\lbrack \frac{V_{k}^{w}\left( {\theta_{t},\phi_{t}} \right)}{{L_{k}^{C}(t)} \times \cos\;\theta} \right\rbrack{\mathbb{d}\Omega}}}} & (59) \\{\eta_{k} = \frac{C_{k}^{nd} \times C_{k}^{w}}{C_{k}^{n} \times C_{k}^{wd}}} & (60)\end{matrix}$

In all cases, the result V may be normalized based on a cryo-cavityreference detector that may simultaneously sample the absolute SIRCUSradiance L_(k) ^(C)(t) at time t (hence for the C_(k) ^(n) measurementthe laser light intensity may be reduced by 5 orders of magnitude).

Accordingly, the SIDCO configuration of the present invention allowsin-flight characterization of an earth viewing NFOV spectrometer to anaccuracy comparable to that of the known incoming solar radiance.Furthermore, the accuracy of SIDCO's earth albedo measurement does notdepend on the accuracy of the known solar spectrum, since that error issystematic in the result A_(k) ^(lbedo)=L_(k) ^(earth)/L_(k) ^(sun).

With the NFOV rotated to view the moon, the present invention alsoallows detailed spectral albedo measurements of the overage lunarsurface. The presence of the WFOV spectrometer also provides redundancyand the ability to maintain benchmark earth spectral measurements, whilethe solar calibration is being performed (i.e. because it will beviewing the earth, while the NFOV is being characterized). Finally, thestability of the calibration parameter η_(k) may also be estimated basedon Monte-Carlo simulations of telescope deformations during and afterlaunch. A flow diagram of a method of the invention, which has beendescribed above, is shown in FIG. 6.

Although the invention is illustrated and described herein withreference to specific embodiments, the invention is not intended to belimited to the details shown. Rather, various modifications may be madein the details within the scope and range of equivalents of the claimsand without departing from the invention.

1. A system for calibrating a spectrometer comprising: widefield-of-view (WFOV) optics providing a first light path to a firstspectrometer, narrow field-of-view (NFOV) optics providing a secondlight path to a second spectrometer, a de-focusing optic selectivelypositioned in the first or second light paths, a scan controller forselectively controlling the WFOV or NFOV optics to scan a celestialbody, and a processor configured to calibrate the de-focusing optic,when the WFOV optics scan the celestial body, and the processorconfigured to calibrate the second spectrometer, when the NFOV opticsand the de-focusing optic scan the celestial body.
 2. The system ofclaim 1 wherein the processor is configured to calibrate the de-focusingoptic, when first, the WFOV optics scan the celestial body without thede-focusing optic positioned in the first light path, and second, theWFOV optics scan the celestial body with the de-focusing opticpositioned in the first light path.
 3. The system of claim 2 wherein theprocessor is configured to calibrate the second spectrometer, after theprocessor calibrates the de-focusing optic.
 4. The system of claim 3wherein the scan controller is configured to control the NFOV optics toscan the earth.
 5. The system of claim 1 wherein the celestial bodyincludes the sun.
 6. The system of claim 1 wherein the scan controlleris configured to provide azimuth and elevation control for rasterscanning the celestial body.
 7. The system of claim 1 including a twosided mirror having one side for reflecting received light in the firstlight path to the first spectrometer, and another side for reflectingreceived light in the second light path to the second spectrometer. 8.The system of claim 1 wherein the de-focusing optic includes one or moreof an un-polarized diffuser, a P-polarized diffuser and an S-polarizeddiffuser.
 9. The system of claim 8 wherein the de-focusing optic ispositioned on a circumferential casing of a housing, and is rotatableabout the circumferential casing for selectively positioning thede-focusing optic in the first or second light paths.
 10. The system ofclaim 1 wherein the NFOV optics and the WFOV optics are oriented toreceive light from two opposing directions, and when the NFOV opticsreceives light from the sun, the WFOV optics receives light from theearth.
 11. A method of calibrating a radiometric system comprising thesteps of: (a) scanning a celestial body using WFOV optics; (b) scanningthe celestial body using NFOV optics; (c) selectively positioning ade-focusing optic to intercept light received by the WFOV optics andlight received by the NFOV optics; (d) calibrating the de-focusing opticusing steps (a) and (c); and (e) calibrating a NFOV imager using steps(b) and (c).
 12. The method of claim 11 including (f) imaging the earthafter calibrating the NFOV imager.
 13. The method of claim 11 whereinthe steps of scanning include raster scanning the celestial body inazimuth and elevation angles.
 14. The method of claim 13 whereinscanning the celestial body includes scanning the sun, while orbitingthe earth.
 15. The method of claim 11 wherein calibrating thede-focusing optic includes the steps of: (i) calibrating a WFOV imager,with the de-focusing optic positioned not to intercept light received bythe WFOV optics, and (ii) calibrating both the WFOV imager and thede-focusing optic, with the de-focusing optic positioned to interceptlight received by the WFOV optics, and (iii) calculating a ratio betweenvalues obtained in steps (i) and (ii).
 16. The method of claim 15wherein calibrating the NFOV imager includes the step of: calibratingthe NFOV imager, after performing step (d).
 17. A method of an imagerviewing a celestial body comprising the steps of: (a) scanning thecelestial body with a predetermined FOV; (b) orbiting the earth, whilethe celestial body is scanned in step (a) to provide an elevation motionto the FOV; and (c) rotating the FOV back and forth, to provide anazimuth motion to the FOV; wherein steps (b) and (c) are effective inproviding a raster scan of the celestial body, and (d) determiningintensity output of the imager by integrating data obtained by theimager while raster scanning the celestial body over angular space andselectively positioning a de-focusing optic to intercept light from thecelestial body.
 18. The method of claim 17 wherein determining intensityoutput of the imager includes multiplying (a) an integral of a pointspread function (PSF) of a detector output of the imager at apredetermined wavelength with (b) an integral of a radiant output of aknown source at the predetermined wavelength.
 19. The method of claim 17wherein the integral of the PSF and the integral of the radiant outputare calculated while orbiting a hemisphere of the earth.
 20. The methodof claim 17 including the steps of: inserting a de-focusing optic in areceived light path of the imager and determining the intensity outputof the imager, and removing the de-focusing optic from the receivedlight path of the imager and determining the intensity output of theimager.